{
  "abstract": "We study clustering of categorical sequences using the Optimal Matching (OM) distance under finite mixtures of finite-state Markov chains. We show that the normalized OM distance between two independent chains converges almost surely to a deterministic population quantity, concentrates exponentially around its finite-horizon mean, and admits an $O(\\sqrt{\\log n/n})$ convergence rate when the two chains have the same transition kernel. These population quantities yield a natural separation condition: the largest within-component limit must be smaller than the smallest between-component limit. Under this condition, hierarchical clustering with any bracketed linkage and Partitioning Around Medoids consistently recover the latent mixture partition. We also propose a consistent estimator of the number of components based on empirical OM distance profiles. The results extend to finite-state hidden Markov models and multichannel categorical observations. Overall, they provide a statistical justification for standard OM-based clustering methods for categorical time series.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21985",
  "author_total": 1,
  "authors": [
    {
      "name": "Ottavio Khalifa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eh8643j6ea1xv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21985",
  "fulltext_url": null,
  "id": "eh8643j6ea1xv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21985",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Bayesian Methods and Mixture Models"
    ]
  ],
  "openalex": "W7213863986",
  "pdf_url": "https://arxiv.org/pdf/2609.21985",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eh8643j6ea1xv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21985",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21985"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Consistency of Optimal Matching-based Clustering for Mixtures of Markov Chains",
  "title_text": "Consistency of Optimal Matching-based Clustering for Mixtures of Markov Chains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:12Z",
  "url": "https://research.draconitic.com/paper/eh8643j6ea1xv",
  "venue": "arXiv",
  "versions": []
}